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This paper uses fractional integration methods to measure the degree of persistence in historical annual data on the world population over the period 1800-2016. The analysis is carried out for the original series, and also for its log transformation and its growth rate. The results indicate that the series considered are highly persistent; in particular, the estimated values of the fractional diffencing parameter are above 1, which implies that shocks have permanent effects. Endogenous break tests detect one main break shortly after WWII. The evidence based on the corresponding sub-sample estimation indicates a sharp fall in the degree of dependence between the observations in the second sub-sample. Although the original data and their log transformation still exhibit explosive behaviour in that sub-sample, the growth rates are mean-reverting, and thus shocks to these series will only have transitory effects; moreover, there is a negative time trend. This has implications for the design of policies aimed at containing population growth.